XVI. SHEAR STRENGTH OF SOIL - Wikispaces · PDF fileShear Strength of Soil Mohr Circle of Stresses In soil testing, cylindrical samples are commonly used in which radial and axial

Soil Mechanics XVI. SHEAR STRENGTH OF SOIL

Soil Mechanics XVI.1. SHEAR STRENGTH OF SOIL

Mohr-Coulomb Failure Criteria

DEFINITION

The maximum or ultimate value of shear stress that can be mobilized

within a soil mass without failure taking place.

The internal resistance per unit area that the soil mass can offer to

resist failure and sliding along any plane inside it.

APPLICATION

Shear Strength can be used for calculating :

– Bearing Capacity of Soil

– Slope Stability

– Lateral Pressure

Shear Strength of Soil

VERTICAL SLOPE RETAINING EARTH WALL

EMBANKMENT LANDSLIDE

GLOBAL FAILURE OF

SHALLOW FOUNDATION

LOCAL FAILURE OF

SHALLOW FOUNDATION

Embankment Strip footing

Soils generally fail in SHEAR

At failure, shear stress along the failure surface (mobilized shear

resistance) reaches the shear strength.

Failure surface

Mobilized shear resistance

Shear Failure in Soils

Retaining wall

Failure surface

Mobilized shear resistance

Soils generally fail in SHEAR

Shear Failure in Soils

At failure, shear stress along the failure surface (mobilized shear

resistance) reaches the shear strength.

At failure, shear stress along the failure surface () reaches the shear

strength (f).

• The soil grains slide over each other along the failure surface.

• No crushing of individual grains.

Shear Failure Mechanism Embankment

FIELD INFLUENCE FACTOR Soil condition : void ratio, particle shape and size

Soil type : Gravel, Sand, Silt, Clay, etc. Water content (especially for clay)

Type of load and its rate

Anisotropic condition

LABORATORY Test method

Sample disturbance

Water content

Strain rate


PARAMETER

Cohesion (c)

Internal Friction Angle ()

CONDITION

Total (c and )

Effective (c’ and ’)

GENERAL EQUATION (MOHR-COULOMB)

= c + n tan or = c’ + (n – u)tan’


COHESIVE SOIL

Has cohesion (c)

Example : Clay, Silt

COHESIONLESS SOIL

Only has internal friction angle () ; c = 0

Example : Sand, Gravel

Shear Strength of Soil Soil Type

COHESION (c)

Sticking together of like materials.

INTERNAL FRICTION ANGLE ()

The stress-dependent component which is similar to sliding friction of two or more soil particles

Shear Strength of Soil Shear Strength Parameter

UNDRAINED SHEAR STRENGTH

Use for analysis of total stress

Commonly = 0 and c = cu

DRAINED SHEAR STRENGTH

Use for analysis of effective stress, with parameter c’, ’

= c’ + (n – u) tan ’

Shear Strength of Soil Shear Strength Parameter

Shear Strength of Soil Mohr Circle of Stresses

In soil testing, cylindrical samples are commonly used in which radial

and axial stresses act on principal planes. The vertical plane is usually

the minor principal plane whereas the horizontal plane is the principal plane. The radial stress (𝜎𝑟) is the minor principal stress (𝜎3), and the

axial stress (𝜎𝑎) is the major principal stress (𝜎1).

Shear Strength of Soil Mohr Circle of Stresses

To visualize the normal and shear stresses acting on any plane within

the soil sample, a graphical representation of stresses called the Mohr

circle is obtained by plotting the principal stresses. The sign

convention in the construction is to consider compressive stresses as

positive and angles measured counter-clockwise also positive.

Shear Strength of Soil Mohr-Coulomb Failure Criteria

When the soil sample has failed, the shear stress on the failure plane

defines the shear strength of the soil. Thus, it is necessary to identify

the failure plane.

Is it the plane on which the maximum shear stress acts, or

is it the plane where the ratio of shear stress to normal stress is the maximum?

For the present, it can be assumed that a failure plane exists and it is

possible to apply principal stresses and measure them in the

laboratory by conducting a triaxial test. Then, the Mohr circle of stress

at failure for the sample can be drawn using the known values of the

principal stresses.


If data from several tests, carried out on different samples up to

failure is available, a series of Mohr circles can be plotted. It is

convenient to show only the upper half of the Mohr circle. A line

tangential to the Mohr circles can be drawn, and is called the Mohr-

Coulomb failure envelope.

f is the maximum shear stress the soil can take without failure, under

normal stress of .

c

Cohesion Friction angle

f

Shear Strength of Soil Total Stress Analysis

𝜏𝑓 = 𝑐 + 𝜎 tan ϕ

f is the maximum shear stress the soil can take without failure, under

normal effective stress of ’.

’

c’

’ Effective

cohesion Effective

friction angle f

’

(u = pore water pressure)

Shear Strength of Soil Effective Stress Analysis

𝜏𝑓 = 𝑐′ + 𝜎′ tan ϕ′ 𝜎′ = 𝜎 − 𝑢

𝜏𝑓 = 𝑐′ + 𝜎′ tan ϕ′

Shear strength consists of two components: cohesive and

frictional.

’

f ’

'

c’ c’

cohesive component

’ tan’

frictional component


Soil elements at different locations

Failure surface

X X

X ~ failure

Y Y

Y ~ stable

’


𝜏𝑓 = 𝑐′ + 𝜎′ tan ϕ′

Y

c

c

c Initially, Mohr circle is a point

c+

The soil element does not fail if

the Mohr circle is contained

within the envelope GL


’

c

GL

As loading progresses, Mohr

circle becomes larger…

…and finally failure occurs

when Mohr circle touches

the envelope


Y

c

c

’

= X

v’

h’ X

u

u +

v’ h’ u v h

X

v

h

σ or σ’

Shear Strength of Soil Total vs Effective Stress Analysis

ϕ’

c’ c

ϕ If X is on failure,

X

𝜎𝑣′

= 𝜎1′

X is on failure

σ’ ϕ’ c’

2'sin

2'cot'

'

3

'

1

'

3

'

1

c

Therefore,

Shear Strength of Soil Mohr-Coulomb Failure Criterion with Mohr Circle of Stress

𝜎ℎ′

= 𝜎3′

(𝜎1′ − 𝜎3

′)

2

(𝜎1′ + 𝜎3

′)

2

𝑐′ cot ∅

𝜎3′ 𝜎1

′

2'sin

2'cot'

'

3

'

1

'

3

'

1

c

'cos'2'sin'

3

'

1

'

3

'

1 c

'cos'2'sin1'sin1 '

3

'

1 c

'sin1

'cos'2

'sin1

'sin1'

3

'

1

c

2

'45tan'2

2

'45tan2'

3

'

1

c

Shear Strength of Soil Mohr-Coulomb Failure Criterion with Mohr Circle of Stress

Shear Strength of Soil Inclination of the Plane of Failure Caused by Shear

Failure → when shear stress on a plane reaches 𝜏𝑓 line

→ determine inclination (θ) of failure plane with major and minor

principal planes

For the soil element shown, determine the normal and shear stresses

on a plane inclined at 35° from the

horizontal axis.

Shear Strength of Soil Example 1

Foil the soil element shown,

determine and .

Shear Strength of Soil Example 2

Soil Mechanics XVI.2. SHEAR STRENGTH OF SOIL

Determination of Shear Strength Parameters

LABORATORY TESTS

Direct Shear Test (DST)

Triaxial (TX) Shear Test (UU, CU, CD)

Unconfined Compression Test (UCT)

FIELD INVESTIGATION

Vane Shear Test (VST)

PARAMETER CORRELATIONS

Cone Penetration Test (SCPT, DCPT)

Standard Penetration Test (SPT) N-Value

California Bearing Ratio (CBR)


Other laboratory tests include, direct simple

shear test, torsional ring shear test, plane strain

triaxial test, laboratory vane shear test,

laboratory fall cone test

Laboratory tests on specimens

taken from representative

undisturbed samples

Field tests

Most common laboratory tests to determine the shear strength parameters are, 1.Direct shear test 2.Triaxial shear test

1. Vane shear test 2. Torvane 3. Pocket penetrometer 4. Fall cone 5. Pressuremeter 6. Static cone penetrometer 7. Standard penetration test

Shear strength parameters of soils

Field conditions

z vc

vc

hc hc

Before construction

A representative soil sample z vc +

hc hc

After and during construction

vc +

Shear Strength of Soil Laboratory Tests

Simulating field conditions in the laboratory

Step 1

Set the specimen in the

apparatus and apply the initial

stress condition

σvc

σvc

σhc σhc

Representative soil

sample taken from

the site

0

0 0

0

Step 2

Apply the corresponding field

stress conditions

σvc + Δσ

σhc σhc

σvc + Δσ

σvc

σvc

Shear Strength of Soil Laboratory Tests

Shear Strength of Soil Direct Shear Test

The test is carried out on a soil

sample confined in a metal box

of square cross-section which is

split horizontally at mid-height. A

small clearance is maintained

between the two halves of the

box. The soil is sheared along a

predetermined plane by moving

the top half of the box relative to

the bottom half. The box is usually square in plan of size 60 mm x 60

mm. A typical shear box is shown.


If the soil sample is fully or partially saturated, perforated metal plates

and porous stones are placed below and above the sample to allow

free drainage. If the sample is dry, solid metal plates are used. A load

normal to the plane of shearing can be applied to the soil sample

through the lid of the box.

Tests on sands and gravels can be performed quickly, and are

usually performed dry as it is found that water does not significantly

affect the drained strength. For clays, the rate of shearing must be

chosen to prevent excess pore pressures building up.


As a vertical normal load is applied to the sample, shear stress is

gradually applied horizontally, by causing the two halves of the box

to move relative to each other. The shear load is measured together

with the corresponding shear displacement. The change of thickness

of the sample is also measured.

A number of samples of the soil are tested each under different

vertical loads and the value of shear stress at failure is plotted against

the normal stress for each test. Provided there is no excess pore

water pressure in the soil, the total and effective stresses will be

identical. From the stresses at failure, the failure envelope can be

obtained.


Specimen is square or

circular

Box splits horizontally in

halves

Normal force applied on top

shear box

Shear force is applied to

move one half of the box

relative to the other (to fail

specimen)


Shear force applied in equal

increments until failure

Failure plane is predetermined

(horizontal)

Horizontal deformation & ΔH is

measured under each load.

Stress-controlled


Constant rate of shear

displacement

Restraining shear force is

measured

Volume changed (ΔH)

Gives ultimate & residual

shear strength

Strain-controlled


For a given test on dry soil, the normal stress can be calculated as,

The resisting shear stress for any shear displacement can be

calculates as,




The test has several advantages:

It is easy to test sands and gravels.

Large samples can be tested in large shear boxes, as small samples can give misleading results due to imperfections such as fractures and fissures, or may not be truly representative.

Samples can be sheared along predetermined planes, when the shear strength along fissures or other selected planes are needed.


The disadvantages of the test include:

The failure plane is always horizontal in the test, and this may not be the weakest plane in the sample. Failure of the soil occurs progressively from the edges towards the centre of the sample.

There is no provision for measuring pore water pressure in the shear box and so it is not possible to determine effective stresses from undrained tests.

The shear box apparatus cannot give reliable undrained strengths because it is impossible to prevent localised drainage away from the shear plane.


Shear Strength of Soil Triaxial Shear Test

The triaxial test is carried out in a

cell on a cylindrical soil sample

having a length to diameter ratio of

2. The usual sizes are 76 mm x 38 mm

and 100 mm x 50 mm. Three principal

stresses are applied to the soil

sample, out of which two are applied

water pressure inside the confining

cell and are equal. The third principal

stress is applied by a loading ram

through the top of the cell and is

different to the other two principal

stresses. A typical triaxial cell is shown.


The soil sample is placed inside a rubber sheath which is sealed to a

top cap and bottom pedestal by rubber O-rings. For tests with pore

pressure measurement, porous discs are placed at the bottom, and

sometimes at the top of the specimen. Filter paper drains may be

provided around the outside of the specimen in order to speed up

the consolidation process. Pore pressure generated inside the

specimen during testing can be measured by means of pressure

transducers.


The triaxial compression test consists of two stages:

First stage: In this, a soil sample is set in the triaxial cell and

confining pressure is then applied.

Second stage: In this, additional axial stress (also called deviator

stress) is applied which induces shear stresses in the sample. The

axial stress is continuously increased until the sample fails.

During both the stages, the applied stresses, axial strain, and pore

water pressure or change in sample volume can be measured.


The triaxial compression test consists of two stages:

Stage 1 Stage 2 Consolidation Stage Shearing Stage



Test Types

There are several test variations, and those used mostly in practice are:

Consolidated-Drained (CD) test: This is similar to CU test except that as

deviator stress is increased, drainage is permitted. The rate of loading

must be slow enough to ensure no excess pore water pressure develops.

CU Consolidated-Undrained (CU) test: In this, drainage is allowed during

cell pressure application. Then without allowing further drainage, deviator

stress is increased keeping cell pressure constant.

Unconsolidated-Undrained (UU) test: In this, cell pressure is applied without

allowing drainage. Then keeping cell pressure constant, deviator stress is

increased to failure without drainage.


CONSOLIDATED-DRAINED (CD) TEST

𝐵 =𝑢𝑐

𝜎3 Skempton’s pore water pressure parameter (B ~ 1.0 for saturated soils)

End of consolidation stage 𝑢𝑐 = 0.

Application of deviator stress, ∆𝜎𝑑:

For drained test ∆𝜎𝑑 is increased slowly, while the drainage valve is kept open,

and any excess pore water pressure generated by ∆𝜎𝑑 is allowed to dissipate.

(ΔV can be measured by measuring amount outflow-water, since S = 100%)

CD test: excess pore water pressure completely dissipated 𝜎3 = 𝜎3′ .

Specimen is subjected to confining stress 𝜎3 all around.

As a result the pore water pressure of the sample increases by 𝑢𝑐.

If the valve is opened at this point the 𝑢𝑐 will dissipate and sample will consolidate (ΔV decreases under 𝜎3)

Stage 1

Stage 2




At failure, total axial stress is same with effective axial stress.

𝜎1 = 𝜎1′=𝜎3

′ + (∆𝜎𝑑)𝑓

𝜎1′→ major principal effective stress at failure

𝜎3′→ minor principal effective stress at failure

Conduct other triaxial (CD) tests under different confining pressure 𝜎3 and obtain the corresponding 𝜎1

′ at failure and plot the Mohr’s circle for each test.





Ᾱ =∆𝑢𝑑

∆𝜎𝑑

End of consolidation stage ∆𝑢𝑐 = 0 (and close valves).

Loose sand and NC clay → ∆𝑢𝑑 increases with strain

Dense sand and OC clay → ∆𝑢𝑑 increases with strain up to a certain point and drops and

becomes negative (due to dilation of soil)

Consolidation of S = 100% sample under confining stress 𝜎3 and allow 𝑢𝑐 to

dissipate.

Drainage valve is closed after complete consolidation (𝑢𝑐 = 0)

Skempton’s pore water pressure parameter

CONSOLIDATED-UNDRAINED (CU) TEST

Stage 1

Stage 2 Deviator stress ∆𝜎𝑑 is applied and increased to failure.

Excess pore water pressure ∆𝑢𝑑 is developed (due to no drainage).


Total and effective principal stresses are not the same.

At failure, measure (∆𝜎𝑑)𝑓 and (∆𝑢𝑑)𝑓.

Major principal stress at failure is obtained as:

Total → 𝜎1 = 𝜎3 + (∆𝜎𝑑)𝑓

Effective → 𝜎1′ = 𝜎1 − (∆𝑢𝑑)𝑓

Minor principal stress at failure is obtained as:

Total → 𝜎3

Effective → 𝜎3′ = 𝜎3 − (∆𝑢𝑑)𝑓









Drainage in both stages is not allowed.

Therefore application of 𝜎3 → 𝑢𝑐 = 𝐵𝜎3 (in Stage 1)

And application of ∆𝜎𝑑 → ∆𝑢𝑑= Ᾱ∆𝜎𝑑 (in Stage 2)

Total pore water pressure, 𝑢 = 𝑢𝑐 + ∆𝑢𝑑 → 𝑢 = 𝐵𝜎3 + Ᾱ∆𝜎𝑑= 𝐵𝜎3 + Ᾱ 𝜎1 − 𝜎3

It can be seen that tests conducted with different 𝜎3 results in the same (∆𝜎𝑑)𝑓 ,

resulting in Mohr’s circle with same radius.

UNCONSOLIDATED-UNDRAINED (UU) TEST


UNCONSOLIDATED-UNDRAINED (UU) TEST

Test Condition

Stage 1 Stage 2

Unconsolidated

Undrained (UU)

Apply confining pressure 3 while the drainage line from the specimen is kept closed (drainage is not

permitted), then the initial pore water pressure (u=uc) is not equal to zero

Apply an added stress d at axial direction. The drainage line from the specimen is still kept closed (drainage is not permitted) (u=Δud0). At failure state

d=(d)f ; pore water pressure u=uf=uc+Δud(f)

Consolidated

Undrained (CU)

Apply confining pressure 3 while the drainage line

from the specimen is opened (drainage is

permitted), then the initial pore water pressure (u=uc) is equal to zero

Apply an added stress d at axial direction. The drainage line from the specimen is kept closed (drainage is not permitted) (u=Δud0). At failure state

d=(d)f ; pore water pressure u=uf=uc+Δud(f)=Δud(f)

Consolidated

Drained (CD)

Apply confining pressure 3 while the drainage line from the specimen is opened (drainage is

permitted), then the initial pore water pressure (u=uc) is equal to zero

Apply an added stress d at axial direction. The drainage line from the specimen is opened (drainage is permitted) so the pore water pressure (u=Δud) is

equal to zero. At failure state d=(d)f; pore water pressure u=uf=uc+Δud(f)=0

3

3

3

3



Significance of Triaxial Testing

The first stage simulates in the laboratory the in-situ condition that soil at different depths is subjected to different effective stresses. Consolidation will occur if the pore water pressure which develops upon application of confining pressure is allowed to dissipate. Otherwise the effective stress on the soil is the confining pressure (or total stress) minus the pore water pressure which exists in the soil.

During the shearing process, the soil sample experiences axial strain, and either volume change or development of pore water pressure occurs. The magnitude of shear stress acting on different planes in the soil sample is different. When at some strain the sample fails, this limiting shear stress on the failure plane is called the shear strength.


The triaxial test has many advantages over the direct shear test:

• The soil samples are subjected to uniform stresses and strains.

• Different combinations of confining and axial stresses can be applied.

• Drained and undrained tests can be carried out.

• Pore water pressures can be measured in undrained tests.

• The complete stress-strain behaviour can be determined.


General Comments

CD: Long-term stability (earth embankments and cut slopes)

CU: Soil initially fully consolidated, then rapid loading (slopes in earth dams

after rapid drawdown)

UU: End of construction stability of saturated clays, load rapidly applied

and no drainage (bearing capacity on soft clays)

SELECTION OF TRIAXIAL TEST

Soil type Type of construction Type of tests and shear strength

Cohesive

Short term (end of construction time)

Triaxial UU or CU for undrained strength with appropriate level of in-situ strength

Staging Construction Triaxial CU for undrained strength with appropriate level of in-situ strength

Long term Triaxial CU with pore water pressure measurement or Triaxial CD for effective shear strength parameter

Granular All Strength parameter ’ which is got from field investigation or direct shear test

Material c- Long Term Triaxial CU with pore water pressure measurement or Triaxial CD for effective shear strength parameter


Shear Strength of Soil Unconfined Compression Test A type of unconsolidated-undrained triaxial test

For clayey samples (cohesive soils)

Confining pressure 𝜎3= 0

Axial load 𝜎1 applied to fail the sample (relatively rapid)

At failure (𝜎3)𝑓 = 0 and (𝜎1)𝑓 = major principal stress

Therefore undrained shear strength is independent of confining

pressure

𝜏1 =𝜎1

2=

𝑞𝑢

2= 𝑐𝑢 𝑜𝑟 𝑠𝑢

where 𝑞𝑢 is the unconfined compressive strength, and 𝑐𝑢(𝑜𝑟 𝑠𝑢) is the

undrained shear strength

Shear Strength of Soil Unconfined Compression Test

Shear Strength of Soil Unconfined Compression Test

Direct shear tests were performed on a dry, sandy soil. The size of the specimen was 50 mm x 50 mm x 20 mm. Tests results were as given in the

table. Find the shear stress parameters.

Test No. Normal Force

(N) Shear Force at

Failure (N)

1 90 54

2 135 82.35

3 315 189.5

4 450 270.5

Problem Set Problem 1

13

Normal Stress, σ

(kPa)

Shear Stress at Failure, τ

(kPa)

36 21.6

54 32.9

126 75.8

180 108.2

For a normally consolidated clay, these are the results of a drained

triaxial test:

chamber confining pressure = 112 kPa

deviator stress at failure = 175 kPa

2.1 Find the angle of internal friction, ø’.

2.2 Determine the angle θ that the failure plane makes with the major principal

plane.

2.3 Find the normal stress σ’ and the shear stress τf on the failure plane.

2.4 Determine the effective normal stress on the plane of maximum shear stress.


13


13

The equation of the effective stress failure envelope for normally consolidated clayey soil is τf = σ’tan30°. A drained triaxial test was

conducted with the same soil at a chamber confining pressure of 70 kPa. Calculate the deviator stress at failure.

The maximum principal stress that causes failure of a cohesive soil specimen in a triaxial test is equal to 220 kPa. The angle of internal

friction is equal to 25°. If the deviator stress at failure is equal to140 kPa. 4.1 Compute the confining chamber pressure .

4.2 Compute the cohesion.

4.3 Compute the shearing stress at failure.


13

An unconsolidated-undrained test was conducted on a saturated clay. The cell pressure was 200 kPa and failure occurred under a

deviatoric stress of 220 kPa. 5.1 Determine the angle of shearing resistance.

5.2 Determine the maximum principal stress at failure.

5.3 Determine the undrained shear strength.


13

A consolidated-undrained soil test was conducted on a normally consolidated sample with a chamber pressure of 140 kPa. The sample

failed when the deviator stress was 124 kPa. The pore water pressure in

the sample at that time was 75 kpa. 6.1 Determine the undrained angle of internal friction.

6.2 Determine the drained angle of internal friction.

6.3 What is the drained angle of internal friction if the soil possess a cohesion of 12

kPa?


13

A sample of sand is subjected to direct shear testing at its normal

water content. Two tests were performed. For one of the tests, the sample fails at a shear stress of 3000 psf when the normal stress is 4000

psf. In the second test, the sample shears at a stress of 4000 psf when

the normal stress is 6000 psf. From these data, 7.1 Determine the angle of internal friction.

7.2 Determine the cohesion.


13

We have the results of two drained triaxial tests on a saturated clay:

Determine the shear strength parameters.


13

Specimen No. σf, kPa (Δσd)f, kPa

1 70 173

2 105 235

When an undrained triaxial compression test was conducted on

specimens of clayey silt, the following results were obtained:

Determine the values of shear parameters considering 9.1) total stresses and 9.2)

effective stresses.


13

Specimen No. σ3, kPa σ1, kPa u, kPa

1 17 157 12

2 44 204 20

3 56 225 22

Embankment constructed rapidly over a soft clay deposit

Example Use of UU Strength in Engineering Practice



Large earth dam constructed rapidly with

no change in water content of clay core


Footing placed rapidly on clay deposit



Embankment raised (2) subsequent to

consolidation under its original height (1)

Example Use of CU Strength in Engineering Practice


Rapid drawdown behind an earth dam

No drainage of the core. Reservoir level falls from 1 2



Rapid construction of an embankment on a natural slope



Embankment constructed very slowly, in layers,

over a soft clay deposit

Example Use of CD Strength in Engineering Practice


Earth dam with steady-state seepage



Excavation or natural slope in clay



CU with pore water

pressure measurement

SELECTION OF SHEAR STRENGTH PARAMETER


Documents

XVI. SHEAR STRENGTH OF SOIL - Wikispaces · PDF fileShear Strength of Soil Mohr Circle of Stresses In soil testing, cylindrical samples are commonly used in which radial and axial